− 1 Krall-Jacobi polynomials

We study a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue equation involving a third order differential operator of Dunkltype.The orthogonality measure of these polynomials consists in the continuous measure of the little -1 Jacobi polynomials to which is added an arbitrary mass located at the point x = 0, the middle of the orthogonality interval.This provides the first nontrivial example of Krall-type polynomials with a point mass inside the orthogonality interval.These polynomials can be obtained by a Geronimus transform of the little q-Jacobi polynomials in the limit q = -1.